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Prove that: (sin(A-B))/(cosAcosB)+(sin...

Prove that:
`(sin(A-B))/(cosAcosB)+(sin(B-C))/(cosBcosc)+(sin(C-A))/(cosCcosA)=0`

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NAGEEN PRAKASHAN ENGLISH-TRIGNOMETRIC FUNCTIONS-EXERCISES 3D
  1. i) If A+B=pi/4 prove that: (cotA-1)(cotB-1)=2

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  2. Prove that: (tan(pi/4+A)+tan(pi/4-A))/(tan(pi/4+A)-tan(pi/4-A))="cos...

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  3. Prove that: (sin(A-B))/(cosAcosB)+(sin(B-C))/(cosBcosc)+(sin(C-A))/(...

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  4. Prove that: sinAsin(B-C)+sinBsin(C-A)+sinCsin(A-B)=0

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  5. Prove that: cot2Acot3A-cot3Acot5A-cot5Acot2A=1

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  6. Prove that: cotA-cot2A="cosec"2A

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  7. Prove that: cos^2A+cos^2B-2cosA\ cos B cos\ (A+B)=sin^2(A+B)

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  8. If tan B=(n sin A cos A)/(1-n cos^(2)A), then tan(A+B) equals to

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  9. If tan B=(n sin A cos A)/(1-n cos^(2)A), then tan(A+B) equals to

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  10. If 2tanB +cotB=tanA, prove that: 2tan(A-B)=cotB

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  11. i) If tan (A+B) = n tan (A-B), prove that: (n+1)/(n-1) = (sin2A)/(sin...

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  12. If A+B=225^(@), then find the value of (cotA)/(1+cotA)xx(cot B)/(1+cot...

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  13. If cos(A+B)sin(C-D)="cos"(A-B)"sin"(C+D) , then write the value of t a...

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  14. If alphaa n dbeta are the solutions of acostheta+bs intheta=c , then s...

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  15. If sinA + sinB = a and cosA+cosB=b, prove that: i) sin(A+B)=(2ab)/(a...

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  16. Prove that the value of 5 costheta+3 cos(theta+pi/3) lies between -7 a...

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  17. Prove that: tan10^(@)tan50^(@)+tan50^(@)tan70^(@)+tan70^(@)tan170^(@...

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  18. prove that sin2x+2sin4x+sin6x=4cos^(2)x.sinx

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  19. Prove that: (sin7A+sin5A+sin9A+sin3A)/(cos3A+cos5A+cos7A+cos9A)= tan...

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  20. Prove that sinA+sin2A+sin4A+sin5A=4 cos(A/2)cos((3A)/2)sin3A

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